$$
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\Aex}{{A_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\tp}{\thinspace .}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
\newcommand{\dfc}{\alpha} % diffusion coefficient
$$
Extensions
These extensions are performed exactly as for a wave equation as they
only affect the spatial derivatives (which are the same as in the
wave equation).
- Variable coefficients
- Neumann and Robin conditions
- 2D and 3D
Future versions of this document will for completeness and
independence of the wave equation document feature info on the three
points. The Robin condition is new, but straightforward to handle:
$$ -\dfc\frac{\partial u}{\partial n} = h_T(u-U_s),\quad
[-\dfc D_x u = h_T(u-U_s)]^n_i
$$
